Chapter 9 - Graph Theory

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Chapter 9. Graph Theory. 9.1 Introduction to Graphs. 9.2 Graph Terminology. 9.3 Represention and Isomorphism. 9.4 Connectivity. 9.5 Euler and Hamilton Paths.
Section 9.0

9.0.1

Chapter

9

Graph Theory 9.1 Introduction to Graphs 9.2 Graph Terminology 9.3 Represention and Isomorphism 9.4 Connectivity 9.5 Euler and Hamilton Paths 9.6* Shortest Path Problems 9.7 Planar Graphs 9.8 Graph Coloring

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.1 Introduction to Graphs

9.1

9.1.1

INTRODUCTION TO GRAPHS

Fig 9.1.1

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.1.2

Chapter 9 Graph Theory

Fig 9.1.2

OPTIONAL FEATURES of GRAPHS

Fig 9.1.3

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.1 Introduction to Graphs

CLASSROOM QUESTION

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.1.3

9.1.4

Chapter 9 Graph Theory

GRAPH-THEORETIC SOFTWARE

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.2 Graph Terminology

9.2

GRAPH TERMINOLOGY DEGREE

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.2.1

9.2.2

Chapter 9 Graph Theory

CLASSROOM EXERCISE

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.2 Graph Terminology

SOCIOLOGICAL APPLICATIONS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.2.3

9.2.4

Chapter 9 Graph Theory

GRAPH THEORETIC DEFINITIONS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.2 Graph Terminology

SPECIAL GRAPHS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.2.5

9.2.6

Chapter 9 Graph Theory

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.2 Graph Terminology

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.2.7

9.2.8

Chapter 9 Graph Theory

REGULAR GRAPHS

CLASSROOM EXERCISES

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.2 Graph Terminology

BIPARTITE GRAPHS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.2.9

9.2.10

Chapter 9 Graph Theory

NEW GRAPHS FROM OLD

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.3 Representations & Isomorphism

9.3.1

9.3 REPRESENTATIONS & ISOMORPHISM INCIDENCE TABLE REPRESENTATION

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.3.2

Chapter 9 Graph Theory

INCIDENCE MATRIX REPRESENTATION

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.3 Representations & Isomorphism

9.3.3

ADJACENCY LIST REPRESENTATION

ADJACENCY MATRIX REPRESENTATION

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.3.4

Chapter 9 Graph Theory

GRAPH ISOMORPHISM

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.3 Representations & Isomorphism

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.3.5

9.3.6

Chapter 9 Graph Theory

SIMPLE ISOMORPHISM

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.3 Representations & Isomorphism

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.3.7

9.3.8

Chapter 9 Graph Theory

GRAPH ISOMORPHISM TESTING

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.3 Representations & Isomorphism

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.3.9

9.3.10

Chapter 9 Graph Theory

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.3 Representations & Isomorphism

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.3.11

Section 9.4 Connectivity

9.4

CONNECTIVITY WALKS and PATHS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.4.1

9.4.2

Chapter 9 Graph Theory

SOME FINE POINTS OF WALKS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.4 Connectivity

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.4.3

9.4.4

Chapter 9 Graph Theory

CYCLE GRAPHS and ISOMORPHISM

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.4 Connectivity

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.4.5

9.4.6

Chapter 9 Graph Theory

CONNECTEDNESS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.4 Connectivity

NAIVE CONNECTEDNESS TEST

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.4.7

9.4.8

Chapter 9 Graph Theory

CUTPOINTS and CUTEDGES

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.5 Euler and Hamilton Tours

9.5.1

9.5 EULER AND HAMILTON TOURS KĂ–NIGSBERG BRIDGE PROBLEM

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.5.2

Chapter 9 Graph Theory

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.5 Euler and Hamilton Tours

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.5.3

9.5.4

Chapter 9 Graph Theory

HAMILTONIAN TOURS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.5 Euler and Hamilton Tours

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.5.5

9.5.6

Chapter 9 Graph Theory

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.5 Euler and Hamilton Tours

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.5.7

Section 9.7 Planar Graphs

9.7

PLANAR GRAPHS

ORIENTABLE SURFACES

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.7.1

9.7.2

Chapter 9 Graph Theory

NONORIENTABLE SURFACES

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.7 Planar Graphs

SPHERE and PLANE

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.7.3

9.7.4

Chapter 9 Graph Theory

JORDAN CURVE THEOREM

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.7 Planar Graphs

KURATOWSKI GRAPHS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.7.5

9.7.6

Chapter 9 Graph Theory

NONPLANARITY of

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.7 Planar Graphs

NONPLANARITY of

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.7.7

9.7.8

Chapter 9 Graph Theory

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.7 Planar Graphs

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.7.9

9.7.10

Chapter 9 Graph Theory

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.7 Planar Graphs

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.7.11

9.7.12

Chapter 9 Graph Theory

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.7 Planar Graphs

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.7.13

9.7.14

Chapter 9 Graph Theory

EDGE-FACE INEQUALITY

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.7 Planar Graphs

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.7.15

9.7.16

Chapter 9 Graph Theory

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.7 Planar Graphs

TWO NONPLANARITY CRITERIA

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.7.17

9.7.18

Chapter 9 Graph Theory

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.8 Graph Coloring

9.8

GRAPH COLORING

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.8.1

9.8.2

Chapter 9 Graph Theory

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.8 Graph Coloring

OBSTRUCTIONS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.8.3

9.8.4

Chapter 9 Graph Theory

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.8 Graph Coloring

APPLICATIONS

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.8.5

9.8.6

Chapter 9 Graph Theory

GREEDY COLORING ALGORITHM

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.8 Graph Coloring

MAP COLORING

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.8.7

9.8.8

Chapter 9 Graph Theory

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.8 Graph Coloring

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

9.8.9

9.8.10

Chapter 9 Graph Theory

coursenotes by Prof. J. L. Gross for Rosen 6th Edition